Maths Teams do Well but Reach Their Limit

Written by Andrew Wrigley, Senior School Mathematics Teacher

Last week, nine Somerset students embarked on a road trip to Hillcrest College for the 2017 QAMT Mathematics quiz. A total of 15 teams from across the Gold Coast competed and a sequential, tangential and occasionally irrational evening ensued.

The quiz is organized into five rounds and is a mixture of team and individual questions. Round One was Estimation with, for example, 'Estimate the number of pecks in a burst of sound from a woodpecker?' (It was almost twice the number I thought). Round Two was Speed, with 12 mental arithmetic problems for the team to complete in two minutes. One such question was, 'What is six minus five multiplied by two?' (The answer is NOT 2; it’s -4). Round Three was Problem Solving with five problems for each team member to solve in 15 minutes, for example, 'If 1.5 chooks can lay 1.5 eggs in 1.5 days, how many chooks can lay a dozen eggs in three days? (Answer, 6). This was a great opportunity for parents and teachers to take some refreshments.

Round Four was Individual questions, for example, 'In a sale, a toy is marked down by 25%. If the toy is $6 cheaper in the sale, how much is it on sale for?' (Answer $18). The final round was General Knowledge, 'How many palindromic numbers are to be found between 100 and 200?' (Answer 10) (101, 111, 121, 131, 141, 151, 161, 171, 181, 191) 'In computing, the term ‘bit’ is an abbreviation of which two terms?' (Answer; binary digit).

The quiz was definitely harder this year with the winning team scoring just 24.5pts out of possible 43. When all the scores were tallied, the Quiz was won by All Saints Anglican School, with TLC second on 22.5 and Kings 3rd on 22. Somerset College #1 was fourth on 21.5 while Somerset College #2 were sixth, so just one point separated 2nd, 3rd and 4th. The top two teams go through to the State final in Brisbane, so Somerset just missed out on another road trip to Brisbane this year.

Congratulations go to all team members, Miku Adachi, Momoe Gondoe, Chloe Ming, Andre Vasquez, Kei Naito, Nathalie Brown, Amaani Besin, Lauren Chan & Marc Hagan.

My thanks go to Mr Brodar, Mr Grocott and Mr Turner for their support on the evening.

The Year 7s are now looking forward to next year’s quiz.

I hope you had the measure of Pythagorean Triple Day last Tuesday 15 August.

Py Tri

A Pythagorean triple represents an integer solution to Pythagoras’ famous theorem for right angled triangles, where a2 + b2 = c2. In this case 82 + 152 = 172. To celebrate the day, the historic Triangle Pub in Seattle (USA), which measures 8m by 15m by 17m was surrounded by Maths enthusiasts in a joint venture between the Museum of Maths in New York and the Seattle’s Pacific Science Centre.

There are only FOUR primitive triples that will convert to dates; (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25), so the next Pythagorean Triple Day will be July 24th 2025. After that you will have a long wait... However, there are also non primitive triples like (6, 8, 10) and (9, 12, 15) which are based on the (3, 4, 5) triple and if we don’t worry about the order of the numbers (so 3/4/5 and 4/3/5 are different), can anyone tell me how many triples of any sort there are each century?

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